Carrier signal phase error estimation

ABSTRACT

A phase error and/or amplitude error of a global positioning system carrier signal is estimated through employment of an optimal minimum variance of the global positioning system carrier signal.

TECHNICAL FIELD

The invention relates generally to navigation systems and moreparticularly to global positioning systems.

BACKGROUND

Global Positioning System (“GPS”) receivers employ a plurality of GPScarrier signals to estimate a location and velocity of the receiver. Thereceivers process the GPS carrier signal, correlate the GPS carriersignal against an emulated carrier and code at base-band, close trackingloops, and output a final measurement for range and range rate. Theprocessing of base-band data is not optimal. Non-linear effects, forexample, large phase error, large amplitude uncertainty, and 50 Hz databit contamination (data stripping is not assumed), must be accounted forto accurately estimate the location and velocity of the GPS receiver. Inconditions of high jamming to signal ratios, determination of non-lineareffects becomes difficult, which reduces accuracy of the estimatedlocation and velocity of the receiver.

Thus, a need exists for an increase in accuracy of estimation ofnon-linear effects of global positioning system carrier signals.

SUMMARY

The invention in one implementation encompasses a method. A phase errorand/or amplitude error of a global positioning system carrier signal isestimated through employment of an optimal minimum variance of theglobal positioning system carrier signal.

DESCRIPTION OF THE DRAWINGS

Features of exemplary implementations of the invention will becomeapparent from the description, the claims, and the accompanying drawingsin which:

FIG. 1 is a representation of an apparatus that comprises a receiver andone or more satellites of a navigation system.

FIG. 2 is a representation of a comparison plot of an arctangentsolution and an optimal solution for a phase error estimation of theapparatus of FIG. 1.

FIG. 3 is a representation of a plot that shows an optimal noisebandwidth for RF noise and receiver clock white noise for the apparatusof FIG. 1.

FIG. 4 is a representation of a plot that shows a phase error sigma atan optimal bandwidth for the apparatus of FIG. 1.

DETAILED DESCRIPTION

Turning to FIG. 1, an apparatus 100 in one example comprises a receiver102 and one or more satellites 104. The receiver 102 in one examplecomprises a global positioning system (“GPS”) receiver. In a furtherexample, the receiver 102 comprises an L1/L2 selective availabilityanti-spoofing module (“SAASM”) receiver. The receiver 102 in one examplecomprises an instance of a recordable data storage medium 108. Thereceiver 102 employs one or more GPS carrier signals 106 from thesatellites 104 to estimate a location and/or velocity of the receiver102. For example, the receiver 102 employs the GPS carrier signals 106to triangulate the location of the receiver 102, as will be understoodby those skilled in the art.

The satellites 104 in one example comprise space vehicles (“SVs”) of anavigation system 110, for example, a global positioning system. Thesatellites 104 orbit the earth and provide the one or more GPS carriersignals 106 to the receiver 102. The GPS carrier signals 106 in oneexample comprise L1 and L2 signals, at 1575.42 megahertz and 1227.60megahertz, respectively. Non-linear effects on the GPS carrier signals106 reduce accuracy of the estimation of the location and/or velocity bythe receiver 102. Exemplary non-linear effects are phase error and/oramplitude error caused by the GPS carrier signals 106 passing throughthe earth's ionosphere. The receiver 102 estimates the phase errorand/or amplitude error to promote an increase in accuracy of estimationof the location and/or velocity of the receiver 102, as will beappreciated by those skilled in the art.

Using conventional early, prompt and late correlators, in-phase I andquadrature Q measurements per SV channel at 1 Khz are given by:I _(E) =ADC(δr+δc _(E)) cos(θ)+noise_(IE)Q _(E) =ADC(δr+δc _(E)) sin(θ)+noise_(QE)I _(P) =ADC(δr) cos(θ)+noise_(IP)Q _(P) =ADC(δr) sin(θ)+noise_(QP)I _(L) =ADC(δr+δc _(L)) cos(θ)+noise_(IL)Q _(L) =ADC(δr+δc _(L)) sin(θ)+noise_(QL)

The measurements are non-linear functions of the unknowns: Amplitude A,code error δr, carrier phase error q, data bit D. In addition, thesignal may become not useful for carrier tracking if the carrier errorexceeds ½ cycle (carrier slip) and invalid for code tracking if the codeerror exceeds a chip. To prevent loss of lock, and to obtain minimumerror, it is desired to extract the optimal amount of information(signal) from the measurements.

Conventional carrier loops use a detector such as an arctan or an I*Qmultiply to eliminate the unknown data bit in conditions where the databit detection becomes unreliable (less than about 25 dBHz C/No). Bothdetectors work well in low noise environments. The arctan is preferredbecause its gain is linear with input phase up to 90 degrees. However,at higher noise levels, the arctan mean output becomes nonlinear, andloses amplitude as well, as will be understood by those skilled in theart.

Other approaches attempt to linearize the observations about anoperating point. Assuming the residual errors are small, thelinearization is valid, which leads to an extended Kalman filterapproach. The Kalman filter would use an observation matrix H taken asthe first derivative of the observations with respect to the states. Toreduce the computational load, the linearized approach is mechanized ina pre-filter which consolidates 1 kHz measurements per channel over 1second. The state estimates from the pre-filter are passed to the mainKalman Filter. There are three difficulties with the extended Kalmanfilter approach: The data is assumed stripped, so that the H matrix canbe formed by differentiation. Secondly, the errors are assumed small sothat linearization is justified. Fixups (non optimal) can be employed totry to mitigate these issues. Finally, the data must be passed to themain Kalman filter, thus introducing possible cascaded filter issues.

General Kalman filter requirements include: optimization criteria isminimum variance; all states must have a normal density function;observation must be linear function of states. The I,Q signals failthese requirements because some states are not normal (phase tends to beflat due to cycle slip, data bit is discrete two-valued) and for largeerrors the observations are extremely non-linear.

A general form of the optimal minimum variance solution for any systemis given as:$\hat{x} = {{E\left\{ {{x❘y} = Y} \right\}} = \frac{\int_{- \infty}^{\infty}{{{Xf}_{x,y}\left( {X,Y} \right)}{\mathbb{d}X}}}{\int_{- \infty}^{\infty}{{f_{x,y}\left( {X,Y} \right)}{\mathbb{d}X}}}}$where {circumflex over (x)} is the minimum variance estimate of x givenobservation y and f(X,Y) is the joint density function of x,y. Thisestimator relaxes the severe Kalman restrictions, but reduces exactly tothe Kalman filter if the Kalman restrictions are imposed. The penalty isthat a closed form solution does not exist—the solution requires theevaluation of an integral in real time, as will be appreciated by thoseskilled in the art.

The general expression of the extended Kalman filter has beenanalytically reduced and is substantially equivalent to:I ₁ =b ₁ cos x+z ₁ I ₂ =b ₂ cos x+z ₂ . . . I _(N) =b _(N) cos x+z _(N)Q ₁ =b ₁ sin x+y ₁ Q ₂ =b ₂ sin x+y ₂ . . . Q _(N) =b _(N) sin x+y _(N)where b_(i) is a data bit, y_(i) and z_(i) are noise bits, and x is thephase of the carrier signal for fifty I,Q prompt observations, whichwould apply for 1 second assuming each observation is summed down from 1kHz to 50 Hz (summed over a data bit assuming bit sync), as will beappreciated by those skilled in the art.

Turning to FIG. 2, plots 202 and 204 show a comparison of an arctanestimator and the optimal estimator. For low noise, the optimal minimumvariance solution tracks the arctan. As the noise increases, and as theassumed statistics of the phase error increases, the optimal solutionprovides a better estimate. The plots 202 and 204 show the densityfunctions of the residuals. In this case, the optimal solution sigma issmaller by a factor of two, and has smaller non-normal outliers.

A similar approach can be used to estimate the signal amplitude A. Aphase estimator {circumflex over (x)} and an amplitude estimator â aregiven by:$\hat{x} = \frac{\int_{{- X}\quad\max}^{X\quad\max}{{{Xf}_{x}(X)}{\prod\limits_{i = 1}^{N}{P_{i}{\mathbb{d}X}}}}}{\int_{{- X}\quad\max}^{X\quad\max}{{f_{x}(X)}{\prod\limits_{i = 1}^{N}{P_{i}{\mathbb{d}X}}}}}$$\hat{a} = \frac{\int_{{- A}\quad\max}^{A\quad\max}{{{Af}_{a}(A)}{\prod\limits_{i = 1}^{N}{P_{i}{\mathbb{d}A}}}}}{\int_{{- A}\quad\max}^{A\quad\max}{{f_{a}(A)}{\prod\limits_{i = 1}^{N}{P_{i}{\mathbb{d}A}}}}}$where P_(i) is defined as a pair term for a pair of the I_(i) and Q_(i)values:$P_{i} = {{\mathbb{e}}^{\frac{- 1}{2\sigma_{y}^{2}}{\lbrack{{({Q_{i} + {A\quad\sin\quad X}})}^{2} + {({I_{i} + {A\quad\cos\quad X}})}^{2}}\rbrack}} + {\mathbb{e}}^{\frac{- 1}{2\sigma_{y}^{2}}{\lbrack{{({Q_{i} - {A\quad\sin\quad X}})}^{2} + {({I_{i} - {A\quad\cos\quad X}})}^{2}}\rbrack}}}$The phase estimator assumes amplitude is known and the amplitudeestimator assumes phase is known. A solution (some what compromised fromoptimal) could be formed by looping thru both solutions.

In another example, both phase and amplitude solutions are optimal, buteach requires a double integral:$\hat{x} = {\frac{\int_{{- X}\quad\max}^{X\quad\max}{{{{Xf}_{x}(X)}\left\lbrack {\int_{{- A}\quad\max}^{A\quad\max}{{{Af}_{a}(A)}{\prod\limits_{i = 1}^{N}{P_{i}{\mathbb{d}A}}}}} \right\rbrack}{\mathbb{d}X}}}{\int_{{- X}\quad\max}^{X\quad\max}{{{f_{x}(X)}\left\lbrack {\int_{{- A}\quad\max}^{A\quad\max}{{f_{a}(A)}{\prod\limits_{i = 1}^{N}{P_{i}{\mathbb{d}A}}}}} \right\rbrack}{\mathbb{d}X}}}\quad{and}}$$\hat{a} = {\frac{\int_{{- A}\quad\max}^{A\quad\max}{{{{Af}_{a}(A)}\left\lbrack {\int_{{- X}\quad\max}^{X\quad\max}{{{Xf}_{x}(X)}{\prod\limits_{i = 1}^{N}{P_{i}{\mathbb{d}X}}}}} \right\rbrack}{\mathbb{d}A}}}{\int_{{- A}\quad\max}^{A\quad\max}{{{f_{a}(A)}\left\lbrack {\int_{{- X}\quad\max}^{X\quad\max}{{f_{x}(X)}{\prod\limits_{i = 1}^{N}{P_{i}{\mathbb{d}X}}}}} \right\rbrack}{\mathbb{d}A}}}.}$

Ultra-tight implies that the main Kalman Filter and system has completeaccess to the I,Q measurements, and complete control of carrier and codedigitally controlled oscillators of the receiver 102. The conventionalinternal tracking loops using the receiver's 102 chosen gains iscompletely eliminated. Having complete control of the tracking loopsallows enhanced performance even neglecting the additional improvementfrom optimal usage of the I,Q data. For example, using a conventionalI,Q detector, with Kalman gains weighted by C/No, improved performanceis obtained.

Turning to FIG. 3, plot 302 shows an exemplary optimal noise bandwidth(in steady-state) for noise sources RF noise (as given by C/No) shownalong the x axis, and receiver clock white noise, characterized bynormalized root-Allen Variance at 1 second Allen Variance separationinterval shown as two parameterized conditions. In addition, each plotseparates into data stripped or non-stripped performance. Clearly, witha given clock model, knowledge of a smaller C/No will allow thebandwidth to drop for minimum. Turning to FIG. 4, plot 402 shows anexemplary minimum phase error sigma at the optimal bandwidth. Withenhanced processing, and using the full Kalman filter, the gain controlto the tracking loops may be more finely tuned. Plots 302 and 402 alsoshow the advantage of a lower noise receiver clock.

Other significant error sources include the clock g-sensitivity, and theinertial measurement unit (“IMU”) accelerometer g-sensitivity. Both gsensitive errors can be partly mitigated by including a g-sensitiveclock state and a g-sensitive accelerometer state in the main Kalman. Inaddition to partly estimating the errors themselves, the states provideknowledge to the Kalman to properly control the tracking loops. Forexample, a very large acceleration over a short time would drive off thecode and phase error. Instead of reinitializing search, the Kalman wouldsimply pick up tracking the code (assuming the error is less than achip), and resume tracking the carrier on whatever cycle it was leftwith. Accelerometer g-sensitive errors may be more severe: A largeacceleration over a short time may produce an I, Q transient that cannotbe observed given a low C/No environment. The resulting residual IMUvelocity error may cause difficulty in resuming carrier tracking. Hereagain, optimal processing will help recover tracking.

The apparatus 100 in one example comprises a plurality of componentssuch as one or more of electronic components, hardware components, andcomputer software components. A number of such components can becombined or divided in the apparatus 100. An exemplary component of theapparatus 100 employs and/or comprises a set and/or series of computerinstructions written in or implemented with any of a number ofprogramming languages, as will be appreciated by those skilled in theart.

The apparatus 100 in one example employs one or more computer-readablesignal-bearing media. Examples of a computer-readable signal-bearingmedium for the apparatus 100 comprise the recordable data storage medium108 of the receiver 102. For example, the computer-readablesignal-bearing medium for the apparatus 100 comprises one or more of amagnetic, electrical, optical, biological, and atomic data storagemedium. In one example, the computer-readable signal-bearing mediumcomprises a modulated carrier signal transmitted over a networkcomprising or coupled with the apparatus 100, for instance, one or moreof a telephone network, a local area network (“LAN”), the internet, anda wireless network.

The steps or operations described herein are just exemplary. There maybe many variations to these steps or operations without departing fromthe spirit of the invention. For instance, the steps may be performed ina differing order, or steps may be added, deleted, or modified.

Although exemplary implementations of the invention have been depictedand described in detail herein, it will be apparent to those skilled inthe relevant art that various modifications, additions, substitutions,and the like can be made without departing from the spirit of theinvention and those are therefore considered to be within the scope ofthe invention as defined in the following claims.

1. A method, comprising the steps of: estimating a phase error and/oramplitude error of a global positioning system (GPS) carrier signalthrough employment of an optimal minimum variance of the GPS carriersignal.
 2. The method of claim 1, wherein the step of estimating thephase error and/or amplitude error of the GPS carrier signal throughemployment of the optimal minimum variance solution comprises the stepof: determining an optimal minimum variance of the GPS carrier signalthrough employment of a plurality of pairs of in-phase terms I_(i) andquadrature terms Q_(i) that are based on the GPS carrier signal.
 3. Themethod of claim 2, wherein the step of determining the optimal minimumvariance of the GPS carrier signal through employment of the pluralityof in-phase and quadrature terms that are based on the GPS carriersignal comprises the step of: calculating a plurality of pair termsP_(i) based on the plurality of pairs of in-phase terms I_(i) andquadrature terms Q_(i):$P_{i} = {{\mathbb{e}}^{\frac{- 1}{2\sigma_{y}^{2}}{\lbrack{{({Q_{i} + {A\quad\sin\quad X}})}^{2} + {({I_{i} + {A\quad\cos\quad X}})}^{2}}\rbrack}} + {\mathbb{e}}^{\frac{- 1}{2\sigma_{y}^{2}}{\lbrack{{({Q_{i} - {A\quad\sin\quad X}})}^{2} + {({I_{i} - {A\quad\cos\quad X}})}^{2}}\rbrack}}}$calculating a phase error estimate {circumflex over (x)} and/or anamplitude error estimate â based on the plurality of pair terms P_(i).4. The method of claim 3, wherein the plurality of pairs of in-phaseterms and quadrature terms comprises N terms, wherein the step ofcalculating the phase error estimate {circumflex over (x)} and/or theamplitude error estimate a based on the plurality of pair terms P_(i)comprises the steps of: calculating the phase error estimate:${\hat{x} = \frac{\int_{{- X}\quad\max}^{X\quad\max}{{{Xf}_{x}(X)}{\prod\limits_{i = 1}^{N}{P_{i}{\mathbb{d}X}}}}}{\int_{{- X}\quad\max}^{X\quad\max}{{f_{x}(X)}{\prod\limits_{i = 1}^{N}{P_{i}{\mathbb{d}X}}}}}};{and}$calculating the amplitude error estimate:$\hat{a} = {\frac{\int_{{- A}\quad\max}^{A\quad\max}{{{Af}_{a}(A)}{\prod\limits_{i = 1}^{N}{P_{i}{\mathbb{d}A}}}}}{\int_{{- A}\quad\max}^{A\quad\max}{{f_{a}(A)}{\prod\limits_{i = 1}^{N}{P_{i}{\mathbb{d}A}}}}}.}$5. The method of claim 3, wherein the plurality of pairs of in-phaseterms and quadrature terms comprises N terms, wherein the step ofcalculating the phase error estimate {circumflex over (x)} and/or theamplitude error estimate a based on the plurality of pair terms P_(i)comprises the steps of: calculating the phase error estimate:${\hat{x} = \frac{\int_{{- X}\quad\max}^{X\quad\max}{{{{Xf}_{x}(X)}\left\lbrack {\int_{{- A}\quad\max}^{A\quad\max}{{{Af}_{a}(A)}{\prod\limits_{i = 1}^{N}{P_{i}{\mathbb{d}A}}}}} \right\rbrack}{\mathbb{d}X}}}{\int_{{- X}\quad\max}^{X\quad\max}{{{f_{x}(X)}\left\lbrack {\int_{{- A}\quad\max}^{A\quad\max}{{f_{a}(A)}{\prod\limits_{i = 1}^{N}{P_{i}{\mathbb{d}A}}}}} \right\rbrack}{\mathbb{d}X}}}};{and}$calculating the amplitude error estimate:$\hat{a} = {\frac{\int_{{- A}\quad\max}^{A\quad\max}{{{{Af}_{a}(A)}\left\lbrack {\int_{{- X}\quad\max}^{X\quad\max}{{{Xf}_{x}(X)}{\prod\limits_{i = 1}^{N}{P_{i}{\mathbb{d}X}}}}} \right\rbrack}{\mathbb{d}A}}}{\int_{{- A}\quad\max}^{A\quad\max}{{{f_{a}(A)}\left\lbrack {\int_{{- X}\quad\max}^{X\quad\max}{{f_{x}(X)}{\prod\limits_{i = 1}^{N}{P_{i}{\mathbb{d}X}}}}} \right\rbrack}{\mathbb{d}A}}}.}$6. A method implemented in a global positioning system (GPS) receiverfor optimizing the extraction of information from received GPS carriersignals comprising the steps of: receiving GPS carrier signals that aresubject to non-linear effects; determining an optimal minimum varianceof the GPS carrier signals using a Kalman filter based on a plurality ofpairs of in-phase terms I_(i) and quadrature terms Q_(i) that representthe GPS carrier signals; estimating a phase error and/or amplitude errorof the GPS carrier signals based on the optimal minimum variance of theGPS carrier signals; applying the estimated phase and/or amplitude errorof the GPS carrier signals to correct the corresponding phase and/oramplitude of the received GPS carrier signals.
 7. The method of claim 6further comprising the step of pre-filtering the in-phase and quadratureterms by consolidating a plurality of measurements of the in-phase andquadrature terms taken at a first sample rate into a singlecorresponding measurement of the in-phase and quadrature terms, thedetermining of the optimal minimum variance of the GPS carrier signalsusing a Kalman filter based on the single corresponding measurement ofthe in-phase and quadrature terms to reduce computational load on aprocessing unit of the GPS receiver.
 8. The method of claim 6 whereinthe step of estimating a phase error and/or amplitude error of the GPScarrier signals based on the optimal minimum variance of the GPS carriersignals generates phase and/or amplitude error estimates that providemore accurate estimates of the corresponding errors than error estimatesmade by using an arctan method.
 9. The method of claim 8 wherein theaccuracy of the phase and/or amplitude error estimates made by saidestimating step as compared with the error estimates made using thearctan method increases as signal-to-noise of the received GPS carriersignals decreases.
 10. The method of claim 6 further comprising the stepof providing the Kalman filter with complete access to pairs of in-phaseterms I_(i) and quadrature terms Q_(i).
 11. The method of claim 10wherein the Kalman filter has direct access to pairs of in-phase termsI_(i) and quadrature terms Q_(i).
 12. The method of claim 10 furthercomprising the steps of: generating injection signals with digitallycontrolled oscillators that are combined with the received GPS carriersignals as part of recovery of GPS information from the GPS carriersignals; and controlling the digitally controlled oscillators directlyby the optimal minimum variance of the GPS carrier signals as determinedby the Kalman filter.
 13. The method of claim 6 wherein said step ofdetermining comprises the step of: calculating a plurality of pair termsP_(i) based on the plurality of pairs of in-phase terms I_(i) andquadrature terms Q_(i):$P_{i} = {{\mathbb{e}}^{\frac{- 1}{2\sigma_{y}^{2}}{\lbrack{{({Q_{i} + {A\quad\sin\quad X}})}^{2} + {({I_{i} + {A\quad\cos\quad X}})}^{2}}\rbrack}} + {\mathbb{e}}^{\frac{- 1}{2\sigma_{y}^{2}}{\lbrack{{({Q_{i} - {A\quad\sin\quad X}})}^{2} + {({I_{i} - {A\quad\cos\quad X}})}^{2}}\rbrack}}}$calculating a phase error estimate {circumflex over (x)} and/or anamplitude error estimate â based on the plurality of pair terms P_(i).14. The method of claim 13, wherein the plurality of pairs of in-phaseterms and quadrature terms comprises N terms, wherein the step ofcalculating the phase error estimate {circumflex over (x )} and/or theamplitude error estimate â based on the plurality of pair terms P_(i)comprises the steps of: calculating the phase error estimate:${\hat{x} = \frac{\int_{{- \chi}\quad\max}^{\chi\quad\max}{{{Xf}_{x}(X)}{\prod\limits_{i = 1}^{N}\quad{P_{i}\quad{\mathbb{d}X}}}}}{\int_{{- \chi}\quad\max}^{\chi\quad\max}{{f_{x}(X)}{\prod\limits_{i = 1}^{N}\quad{P_{i}\quad{\mathbb{d}X}}}}}};{and}$calculating the amplitude error estimate:$\hat{a} = {\frac{\int_{{- A}\quad\max}^{A\quad\max}{{{Af}_{a}(A)}{\prod\limits_{i = 1}^{N}\quad{P_{i}\quad{\mathbb{d}A}}}}}{\int_{{- A}\quad\max}^{A\quad\max}{{f_{a}(A)}{\prod\limits_{i = 1}^{N}\quad{P_{i}\quad{\mathbb{d}A}}}}}.}$15. The method of claim 13 wherein the plurality of pairs of in-phaseterms and quadrature terms comprises N terms, wherein the step ofcalculating the phase error estimate {circumflex over (x)} and/or theamplitude error estimate â based on the plurality of pair terms P_(i)comprises the steps of: calculating the phase error estimate:${\hat{x} = \frac{\int_{{- \chi}\quad\max}^{\chi\quad\max}{{{{Xf}_{x}(X)}\left\lbrack {\int_{{- A}\quad\max}^{A\quad\max}{{{Af}_{a}(A)}{\prod\limits_{i = 1}^{N}\quad{P_{i}\quad{\mathbb{d}A}}}}} \right\rbrack}\quad{\mathbb{d}X}}}{\int_{{- \chi}\quad\max}^{\chi\quad\max}{{{f_{x}(X)}\left\lbrack {\int_{{- A}\quad\max}^{A\quad\max}{{f_{a}(A)}{\prod\limits_{i = 1}^{N}\quad{P_{i}\quad{\mathbb{d}A}}}}} \right\rbrack}\quad{\mathbb{d}X}}}};{and}$calculating the amplitude error estimate:$\hat{a} = {\frac{\int_{{- A}\quad\max}^{A\quad\max}{{{{Af}_{a}(A)}\left\lbrack {\int_{{- \chi}\quad\max}^{\chi\quad\max}{{{Xf}_{x}(X)}{\prod\limits_{i = 1}^{N}\quad{P_{i}\quad{\mathbb{d}X}}}}} \right\rbrack}\quad{\mathbb{d}A}}}{\int_{{- A}\quad\max}^{A\quad\max}{{{f_{a}(A)}\left\lbrack {\int_{{- \chi}\quad\max}^{\chi\quad\max}{{f_{x}(X)}{\prod\limits_{i = 1}^{N}\quad{P_{i}\quad{\mathbb{d}X}}}}} \right\rbrack}\quad{\mathbb{d}A}}}.}$16. A global positioning system (GPS) receiver for optimizing theextraction of information from received GPS carrier signals comprising:means for receiving GPS carrier signals that are subject to non-lineareffects; means, coupled to the receiving means, for determining anoptimal minimum variance of the received GPS carrier signals using aKalman filter based on a plurality of pairs of in-phase terms I_(i) andquadrature terms Q_(i) that represent the GPS carrier signals; means,coupled to the determining means, for estimating a phase error and/oramplitude error of the GPS carrier signals based on the optimal minimumvariance of the GPS carrier signals; means, coupled to the estimatingmeans, for applying the estimated phase and/or amplitude error of theGPS carrier signals to correct the corresponding phase and/or amplitudeof the received GPS carrier signals.
 17. The receiver of claim 16further comprising means for pre-filtering the in-phase and quadratureterms by consolidating a plurality of measurements of the in-phase andquadrature terms taken at a first sample rate into a singlecorresponding measurement of the in-phase and quadrature terms, thedetermining means determining of the optimal minimum variance of the GPScarrier signals using a Kalman filter based on the single correspondingmeasurement of the in-phase and quadrature terms to reduce computationalload on a processing unit of the GPS receiver.
 18. The receiver of claim16 wherein the estimating means estimates a phase error and/or amplitudeerror of the GPS carrier signals based on the optimal minimum varianceof the GPS carrier signals generates phase and/or amplitude errorestimates that provide more accurate estimates of the correspondingerrors than error estimates made by using an arctan method.
 19. Thereceiver of claim 18 wherein the estimating means provides an accuracyof the phase and/or amplitude error estimates that increases assignal-to-noise of the received GPS carrier signals decreases ascompared with an error estimate made using the arctan method.
 20. Thereceiver of claim 16 wherein the determining means provides the Kalmanfilter with complete access to pairs of in-phase terms I_(i) andquadrature terms Q_(i).
 21. The receiver of claim 20 wherein the Kalmanfilter has direct access to pairs of in-phase terms I_(i) and quadratureterms Q_(i).
 22. The receiver of claim 20 further comprising: means forgenerating injection signals with digitally controlled oscillators thatare combined with the received GPS carrier signals as part of recoveryof GPS information from the GPS carrier signals; and means forcontrolling the digitally controlled oscillators directly by the optimalminimum variance of the GPS carrier signals as determined by the Kalmanfilter.
 23. The receiver of claim 16 wherein said determining meanscomprises: means for calculating a plurality of pair terms P_(i) basedon the plurality of pairs of in-phase terms I_(i) and quadrature termsQ_(i):$P_{i} = {e^{\frac{- 1}{2\sigma_{y}^{2}}{\lbrack{{({Q_{i} + {A\quad\sin\quad X}})}^{2} + {({I_{i} + {A\quad\cos\quad X}})}^{2}}\rbrack}} + e^{\frac{- 1}{2\sigma_{y}^{2}}{\lbrack{{({Q_{i} - {A\quad\sin\quad x}})}^{2} + {({I_{i} - {A\quad\cos\quad X}})}^{2}}\rbrack}}}$means for calculating a phase error estimate {circumflex over (x)}and/or an amplitude error estimate â based on the plurality of pairterms P_(i).
 24. The receiver of claim 23, wherein the plurality ofpairs of in-phase terms and quadrature terms comprises N terms, whereinthe calculating means calculates the phase error estimate {circumflexover (x)} and/or the amplitude error estimate â based on the pluralityof pair terms P_(i) comprises: means for calculating the phase errorestimate:${\hat{x} = \frac{\int_{{- \chi}\quad\max}^{\chi\quad\max}{{{Xf}_{x}(X)}{\prod\limits_{i = 1}^{N}\quad{P_{i}\quad{\mathbb{d}X}}}}}{\int_{{- \chi}\quad\max}^{\chi\quad\max}{{f_{x}(X)}{\prod\limits_{i = 1}^{N}\quad{P_{i}\quad{\mathbb{d}X}}}}}};{and}$means for calculating the amplitude error estimate:$\hat{a} = {\frac{\int_{{- A}\quad\max}^{A\quad\max}{{{Af}_{a}(A)}{\prod\limits_{i = 1}^{N}\quad{P_{i}\quad{\mathbb{d}A}}}}}{\int_{{- A}\quad\max}^{A\quad\max}{{f_{a}(A)}{\prod\limits_{i = 1}^{N}\quad{P_{i}\quad{\mathbb{d}A}}}}}.}$25. The receiver of claim 23 wherein the plurality of pairs of in-phaseterms and quadrature terms comprises N terms, wherein the calculatingmeans calculates the phase error estimate {circumflex over (x)} and/orthe amplitude error estimate â based on the plurality of pair termsP_(i) comprises: means for calculating the phase error estimate:${\hat{x} = \frac{\int_{{- \chi}\quad\max}^{\chi\quad\max}{{{{Xf}_{x}(X)}\left\lbrack {\int_{{- A}\quad\max}^{A\quad\max}{{{Af}_{a}(A)}{\prod\limits_{i = 1}^{N}\quad{P_{i}\quad{\mathbb{d}A}}}}} \right\rbrack}\quad{\mathbb{d}X}}}{\int_{{- \chi}\quad\max}^{\chi\quad\max}{{{f_{x}(X)}\left\lbrack {\int_{{- A}\quad\max}^{A\quad\max}{{f_{a}(A)}{\prod\limits_{i = 1}^{N}\quad{P_{i}\quad{\mathbb{d}A}}}}} \right\rbrack}\quad{\mathbb{d}X}}}};{and}$means for calculating the amplitude error estimate:$\hat{a} = {\frac{\int_{{- A}\quad\max}^{A\quad\max}{{{{Af}_{a}(A)}\left\lbrack {\int_{{- \chi}\quad\max}^{\chi\quad\max}{{{Xf}_{x}(X)}{\prod\limits_{i = 1}^{N}\quad{P_{i}\quad{\mathbb{d}X}}}}} \right\rbrack}\quad{\mathbb{d}A}}}{\int_{{- A}\quad\max}^{A\quad\max}{{{f_{a}(A)}\left\lbrack {\int_{{- \chi}\quad\max}^{\chi\quad\max}{{f_{x}(X)}{\prod\limits_{i = 1}^{N}\quad{P_{i}\quad{\mathbb{d}X}}}}} \right\rbrack}\quad{\mathbb{d}A}}}.}$